Three-point boundary value problems of nonlinear second-order q -difference equations involving different numbers of q

We study a new class of three-point boundary value problems of nonlinear second-order q-difference equations. our problems contain different numbers of q in derivatives and integrals. by using a variety of fixed point theorems (such as banach's contraction principle,boyd and wong fixed point theorem for nonlinear contractions,krasnoselskii's fixed point theorem,and leray-schauder nonlinear alternative) and leray-schauder degree theory,some new existence and uniqueness results are obtained. illustrative examples are also presented. © 2013 thanin sitthiwirattham et al.